
"""simple docstring"""


from . import (
    albert,
    align,
    altclip,
    audio_spectrogram_transformer,
    auto,
    autoformer,
    bark,
    bart,
    barthez,
    bartpho,
    beit,
    bert,
    bert_generation,
    bert_japanese,
    bertweet,
    big_bird,
    bigbird_pegasus,
    biogpt,
    bit,
    blenderbot,
    blenderbot_small,
    blip,
    blip_a,
    bloom,
    bridgetower,
    byta,
    camembert,
    canine,
    chinese_clip,
    clap,
    clip,
    clipseg,
    codegen,
    conditional_detr,
    convbert,
    convnext,
    convnextva,
    cpm,
    cpmant,
    ctrl,
    cvt,
    dataavec,
    deberta,
    deberta_va,
    decision_transformer,
    deformable_detr,
    deit,
    deprecated,
    deta,
    detr,
    dialogpt,
    dinat,
    distilbert,
    dit,
    donut,
    dpr,
    dpt,
    efficientformer,
    efficientnet,
    electra,
    encodec,
    encoder_decoder,
    ernie,
    ernie_m,
    esm,
    falcon,
    flaubert,
    flava,
    fnet,
    focalnet,
    fsmt,
    funnel,
    git,
    glpn,
    gpta,
    gpt_bigcode,
    gpt_neo,
    gpt_neox,
    gpt_neox_japanese,
    gpt_swa,
    gptj,
    gptsan_japanese,
    graphormer,
    groupvit,
    herbert,
    hubert,
    ibert,
    imagegpt,
    informer,
    instructblip,
    jukebox,
    layoutlm,
    layoutlmva,
    layoutlmva,
    layoutxlm,
    led,
    levit,
    lilt,
    llama,
    longformer,
    longta,
    luke,
    lxmert,
    mam_aaa,
    marian,
    markuplm,
    maskaformer,
    maskformer,
    mbart,
    mbartaa,
    mega,
    megatron_bert,
    megatron_gpta,
    mgp_str,
    mluke,
    mobilebert,
    mobilenet_va,
    mobilenet_va,
    mobilevit,
    mobilevitva,
    mpnet,
    mra,
    mta,
    musicgen,
    mvp,
    nat,
    nezha,
    nllb,
    nllb_moe,
    nystromformer,
    oneformer,
    open_llama,
    openai,
    opt,
    owlvit,
    pegasus,
    pegasus_x,
    perceiver,
    phobert,
    pixastruct,
    plbart,
    poolformer,
    prophetnet,
    qdqbert,
    rag,
    realm,
    reformer,
    regnet,
    rembert,
    resnet,
    roberta,
    roberta_prelayernorm,
    roc_bert,
    roformer,
    rwkv,
    sam,
    segformer,
    sew,
    sew_d,
    speech_encoder_decoder,
    speech_to_text,
    speech_to_text_a,
    speechta,
    splinter,
    squeezebert,
    swiftformer,
    swin,
    swinasr,
    swinva,
    switch_transformers,
    ta,
    table_transformer,
    tapas,
    time_series_transformer,
    timesformer,
    timm_backbone,
    transfo_xl,
    trocr,
    tvlt,
    umta,
    unispeech,
    unispeech_sat,
    upernet,
    videomae,
    vilt,
    vision_encoder_decoder,
    vision_text_dual_encoder,
    visual_bert,
    vit,
    vit_hybrid,
    vit_mae,
    vit_msn,
    vivit,
    wavaveca,
    wavaveca_conformer,
    wavaveca_phoneme,
    wavaveca_with_lm,
    wavlm,
    whisper,
    x_clip,
    xglm,
    xlm,
    xlm_prophetnet,
    xlm_roberta,
    xlm_roberta_xl,
    xlnet,
    xmod,
    yolos,
    yoso,
)







"""simple docstring"""


import numpy as np



def 						lowerCamelCase__      (				UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_ = 1E-12		,   UpperCAmelCase_ = 1_00		,   )->				tuple[float, np.ndarray]:







       """simple docstring"""
       assert np.shape(UpperCAmelCase_					)[0] == np.shape(UpperCAmelCase_					)[1]
       # Ensure proper dimensionality.
       assert np.shape(UpperCAmelCase_					)[0] == np.shape(UpperCAmelCase_					)[0]
       # Ensure inputs are either both complex or both real
       assert np.iscomplexobj(UpperCAmelCase_					) == np.iscomplexobj(UpperCAmelCase_					)
       UpperCamelCase       			=		np.iscomplexobj(UpperCAmelCase_					)
       if is_complex:
              # Ensure complex input_matrix is Hermitian
              assert np.array_equal(UpperCAmelCase_		,   input_matrix.conj().T					)

       # Set convergence to False. Will define convergence when we exceed max_iterations
       # or when we have small changes from one iteration to next.

       UpperCamelCase       			=		False
       UpperCamelCase       			=		0
       UpperCamelCase       			=		0
       UpperCamelCase       			=		1E12

       while not convergence:
              # Multiple matrix by the vector.
              UpperCamelCase       			=		np.dot(UpperCAmelCase_		,   UpperCAmelCase_					)
              # Normalize the resulting output vector.
              UpperCamelCase       			=		w / np.linalg.norm(UpperCAmelCase_					)
              # Find rayleigh quotient
              # (faster than usual b/c we know vector is normalized already)
              UpperCamelCase       			=		vector.conj().T if is_complex else vector.T
              UpperCamelCase       			=		np.dot(UpperCAmelCase_		,   np.dot(UpperCAmelCase_		,   UpperCAmelCase_					)					)

              # Check convergence.
              UpperCamelCase       			=		np.abs(lambda_ - lambda_previous					) / lambda_
              iterations += 1

              if error <= error_tol or iterations >= max_iterations:
                     UpperCamelCase       			=		True

              UpperCamelCase       			=		lambda_

       if is_complex:
              UpperCamelCase       			=		np.real(lambda_					)

       return lambda_, vector



def 						lowerCamelCase__      (				)->				None:







       """simple docstring"""
       UpperCamelCase       			=		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]					)
       UpperCamelCase       			=		np.array([41, 4, 20]					)
       UpperCamelCase       			=		real_input_matrix.astype(np.complexaaa					)
       UpperCamelCase       			=		np.triu(1j * complex_input_matrix		,   1					)
       complex_input_matrix += imag_matrix
       complex_input_matrix += -1 * imag_matrix.T
       UpperCamelCase       			=		np.array([41, 4, 20]					).astype(np.complexaaa					)

       for problem_type in ["real", "complex"]:
              if problem_type == "real":
                     UpperCamelCase       			=		real_input_matrix
                     UpperCamelCase       			=		real_vector
              elif problem_type == "complex":
                     UpperCamelCase       			=		complex_input_matrix
                     UpperCamelCase       			=		complex_vector

              # Our implementation.
              UpperCamelCase			,							UpperCamelCase       			=		power_iteration(UpperCAmelCase_		,   UpperCAmelCase_					)

              # Numpy implementation.

              # Get eigenvalues and eigenvectors using built-in numpy
              # eigh (eigh used for symmetric or hermetian matrices).
              UpperCamelCase			,							UpperCamelCase       			=		np.linalg.eigh(UpperCAmelCase_					)
              # Last eigenvalue is the maximum one.
              UpperCamelCase       			=		eigen_values[-1]
              # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
              UpperCamelCase       			=		eigen_vectors[:, -1]

              # Check our implementation and numpy gives close answers.
              assert np.abs(eigen_value - eigen_value_max					) <= 1E-6
              # Take absolute values element wise of each eigenvector.
              # as they are only unique to a minus sign.
              assert np.linalg.norm(np.abs(UpperCAmelCase_					) - np.abs(UpperCAmelCase_					)					) <= 1E-6


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      test_power_iteration()





